Re: st: simultaneous probit model

Notation is important here. The model you have written down is not
quite model 6 in Maddala. Model 6 has

(1) Y1* = a*Y2* + b*X1 + e1
(2) Y2* = b*Y1* + c*X2 + e2

i.e., the endogenous regressors on the RHS are the latent indices
underlying Y1 and Y2, not the binary indicators themselves. If this is
the model you want, Maddala, on the pages you've cited, outlines a
2-step plug in method. That's straightforward to implement. Standard
errors are more complicated, but you could just bootstrap it all to get
consistent standard errors.

best.
Partha
Marie-Benoit MAGRINI wrote:

Hello,

I am looking for a program allowing me to implement the « model 6 » in
the book of Maddala (1983, “Limited dependent and qualitative
variables in econometrics”, chapter 8 about the two-stage estimation
methods, page 246).

That is, I am trying to estimate the following simultaneous probit
model :

(1) Y1 = a*Y2 + b*X1 + e1
(2) Y2 = b*Y1 + c*X2 + e2

where Y1 and Y2 are two endogeneous binary variables; X1 and X2 are
two sets of exogenous variables of Y1 and Y2 respectively; e1 and e2
the error terms.

Y1 and Y2 are endogenously determined by each other.

I have looked at the ‘cdsimeq’ program but I understand that it
corresponds to the model where one dependent variable is continuous
and the other binary. So it cannot be used in my case.

I have also looked at the ‘biprobit’ procedure but I understand that
it is adapted only for recursive model that is only one dependent
variable is an explicative of the other one (the model 6 I’ve been
trying to estimate is not recursive).

Could someone tell me if this simultaneous probit model can be
estimated with STATA ?